Phase closure retrieval in an
infrared-to-visible upconversion
interferometer for high resolution
astronomical imaging
Damien Ceus,1 Alessandro Tonello,1 Ludovic Grossard,1
Laurent Delage,1 François Reynaud,1,∗ Harald Herrmann,2
and Wolfgang Sohler2
1 XLIM
Département Photonique, Université de Limoges, UMR CNRS 6172, 123 Av. A.
Thomas, 87060 LIMOGES CEDEX, France
2 Universität Paderborn, Angewandte Physik, Warburger Str. 100 - 33098 PADERBORN,
Germany
*[email protected]
Abstract: This paper demonstrates the use of a nonlinear upconversion
process to observe an infrared source through a telescope array detecting the
interferometric signal in the visible domain. We experimentally demonstrate
the possibility to retrieve information on the phase of the object spectrum
of an infrared source by using a three-arm upconversion interferometer.
We focus our study on the acquisition of phase information of the complex
visibility by means of the phase closure technique. In our experimental
demonstration, a laboratory binary star with an adjustable photometric
ratio is used as a test source. A real time comparison between a standard
three-arm interferometer and our new concept using upconversion by sumfrequency generation demonstrates the preservation of phase information
which is essential for image reconstruction.
© 2011 Optical Society of America
OCIS codes: (350.1260) Astronomical optics; (120.3180) Interferometry; (110.1650) Coherence imaging; (070.0070) Fourier optics and signal processing; (060.2310) Fiber optics;
(190.4223) Nonlinear wave mixing; (160.3730) Lithium niobate.
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25 April 2011 / Vol. 19, No. 9 / OPTICS EXPRESS 8616
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1.
Introduction
Currently, the biggest monolithic or segmented optical telescopes such as the Very Large Telescope [1], the Keck [2] or Subaru telescopes [3], have diameters in the range of 10 m. This size
limitation leads to an angular resolution in the range of 0.1 μ rad for a 1 μ m wavelength. To
overcome this problem, it is possible to use the aperture synthesis technique, which was firstly
demonstrated by Michelson [4]. For this purpose, the optical fields collected by two telescopes
Ti T j , spaced by a distance called baseline, are combined together. This two-telescope array
works as a two-arm interferometer, and its highest angular resolution is related to the longest
baseline. These diluted apertures are used to reach nano-radian angular resolution in ground
based observatories such as VLTI [5] and CHARA [6] or in space missions [7]. These kinds of
optical instruments are designed to analyze the spatial angular intensity distribution of an astronomical object. At the output of the interferometer, the detected signal, hereafter called the
interferometric signal, is a fringe pattern modulated by the theoretical complex fringe visibility
Vth = Cth exp( jϕth ). For a pair of telescopes, Cth is the fringe contrast and ϕth the phase, both
related to the object spectrum. As discussed below in this letter, the Zernike Van Cittert theorem
gives a relation between the visibility Vth and the object spatial angular intensity distribution
O(Ω), with Ω the angular separation of the object under test. Figure 1 gives an example of Cth
and ϕth plotted as a function of the normalized baseline. Note that for these two non-symmetric
objects, spectra have the same modulus but different phases. Therefore, the ability to measure
the phase of Vth remains mandatory for non-symmetric image reconstruction. Unfortunately,
atmospheric turbulence and/or instrument instabilities (particularly in space mission) induce
random phase shifts on the visibility function. Consequently, a direct measurement of ϕth is
impossible. To overcome this limitation, Jennison proposed the use of the phase closure technique [8]. The phase closure term is theoretically unaffected by the atmospheric turbulences or
by the instrument instabilities, and allows for example: image reconstruction [9], the detection
of close faint companions in astronomy [10] or the signature of planet transit events [11]. The
phase closure technique can be achieved only with a three (or more) arm interferometer. In this
paper, we report for the first time to our knowledge, the observation of an infrared source by
a sum-frequency conversion interferometer, using the Jennison’s phase closure technique. In
the following, this interferometer will be called upconversion interferometer. In our upconversion interferometer, the infrared light of the object under test, collected by each Ti telescope, is
converted from infrared to visible wavelength. This way, the Vth complex visibility is acquired
in the visible spectral domain. This experimental test has been achieved with a in-laboratory
proof of principle experiment. This type of high angular resolution imaging instrument has to
provide reliable contrasts and phase closure measurements. For this purpose, we took care to
comply with the polarization [12] and spatial filtering [13, 14] requirements related to spatial
coherence analysis. In a first step, we have developed our upconversion interferometer using
telecommunication components to check that Vth is faithfully transfered from infrared to visible wavelength domain. In a previous work, the Ci j contrasts had been retrieved successfully in
a two-arm upconversion interferometer [15]. The core of this paper describes the acquisition of
the phase closure using our three-arm upconversion interferometer.
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Fig. 1. Two different configurations of a non-symmetric object. The contrast and the phase
of the object spectrum are plotted as a function of the normalized baseline between two
telescopes. Without atmospheric turbulences, this phase is not corrupted and can be measured.
2.
Description of the Jennison’s phase closure technique
Figure 2 shows the principle of a one-dimension telescope array able to provide high angular
resolution images for optical astronomy. The object under test is an unbalanced binary star
with a spatial angular intensity distribution O(Ω), where Ω is the angular separation. In our
experimental setup, the binary star and the telescope array are along the same axis, so Ω0 is the
projection of Ω on the axis of the telescope. In the Fig. 2 configuration, the baseline T1 T2 (i.e
the distance between T1 and T2 ) is fixed and equal to b. The distance T2 T3 can be set to nb with
n an integer.
Unbalanced binary star O(W0)
Atmospheric turbulences
j3
W0
j2
j1
T3
One dimensional
telescope array
T2
nb
T1
3 to 1 Interferometer
+ Photometry
b
Delay lines
Optical path
modulators
Couplers
Visibility: Cij and jij
+ random phase term ji
Fig. 2. Overview of a one-dimension telescope interferometer dedicated to high resolution
imaging. O(Ω0 ): spatial angular intensity distribution, Ω0 : angular separation. Ti is the ith
telescope. T3 can be relocated in different positions equal to nb with n an integer and b the
baseline between T1 T2 . Output data: fringe contrasts Ci j and object spectrum phases ϕi j
related to a pair of telescopes Ti T j corrupted by the turbulences phases ϕi at Ti and ϕ j at T j .
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As seen previously, the complex visibility is equal to:
Vth (nb)
= Cth exp( jϕth )
(1)
The Zernike Van Cittert theorem gives the relation between the theoretical complex visibility
Vth (nb) and the classical spatial angular intensity distribution O(Ω), see [16] for more details:
Vth (nb)
=
1
I
ob ject
O(Ω) exp( j2π nbΩ/λIR )dΩ
(2)
where λIR is the mean wavelength of the analyzed radiation and I the total intensity emitted
by the object. Equation (2) shows that the theoretical fringe visibility is equal to the Fourier
Transform of the spatial angular intensity distribution:
Vth (nb) = (1/I)Õ(N)
(3)
with Õ the object spectrum and N = nb/λIR the spatial frequency. As shown on Fig. 2, two
random phases ϕi and ϕ j , related to the atmospheric turbulence, perturb the measurement of ϕth ,
the argument of Vth (nb). Consequently, the experimental phase is shifted by ϕi − ϕ j preventing
the ϕi j measurement:
Vi j
= Ci j exp[ j(ϕi − ϕ j + ϕi j )]
(4)
Hence, each pair of the telescope array cannot provide any exploitable information on ϕi j .
Thanks to Jennison’s proposal, the phase closure technique allows to get a phase information
directly related to the object spectrum phase. Let us describe this method.
In presence of atmospheric disturbances, the experimental complex visibility Vi j is given by
Eq. (4). The phase closure φ is the linear combination of the arguments of the three experimental
complex visibilities V12 , V23 and V31 related to the pairs of telescopes T1 T2 , T2 T3 and T3 T1
respectively:
φ
= (ϕ1 − ϕ2 + ϕ12 ) + (ϕ2 − ϕ3 + ϕ23 ) + (ϕ3 − ϕ1 + ϕ31 )
= ϕ12 + ϕ23 + ϕ31
(5)
The phase closure information is free of atmospheric disturbances.
The following part is dedicated to the description of an upconversion interferometer and how
the phase closure technique was implemented.
3.
Test of a laboratory high angular resolution upconversion interferometer
In this proof-of-principle experiment, the frequency upconversion took place in each arm of
the upconversion interferometer. All the optical devices used in our test bench are polarization
maintaining components and spatially single-mode. The wavelength conversion of a 1541 nm
laboratory star to 630 nm was achieved in a Periodically Poled Lithium Niobate (PPLN) waveguide pumped by a 1064 nm YAG laser.
As seen previously, the phase closure technique requires at least, a three arm interferometer,
so a third interferometric arm was added to our previous test bench. In order to demonstrate
that the phase closure information can be transferred from the infrared to the visible spectral
domain, we designed and implemented the three telescope interferometers as shown in Fig. 3.
The experimental setup can be split up into four main subsystems:
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a) The stars simulator: in our experimental configuration, the test-object is a binary star.
b) The telescopes array: three telescopes in a one-dimension linear configuration.
c) The infrared interferometer: classical interferometer in the infrared region used as a reference.
d) The upconversion interferometer: our new instrument under test.
Fig. 3. Experimental setup of the upconversion test bench. DFB: Distributed Feed Back
laser at 1541 nm, CL: Collimating Lens, nb the baseline between a pair of telescopes Ti T j
with n an integer, Mux: allows the combination of the signal at 1541 nm and 1064 nm,
PPLN: Periodically Pooled Niobate Lithium, MAFL: Multi-Aperture Fibre Linked Interferometer, T( ˚ C): temperature controller, IF: Interference Filter at λ = 630 nm ± 20 nm,
L: Lens. The delay lines are used for precision optical path length control in the infrared
and visible interferometers.
For our proof of principle experiment, we used telecommunication wavelength sources and
components for practical and cost reasons. Nonetheless, these experimental results can be transposed to other wavelength domains. In our experiment, the object to be imaged was an unbalanced laboratory binary star. For this purpose, a 1 to 2 fibre coupler, with an adjustable photometric ratio called μ , allowed to route the optical light emitted by a distributed feed back laser
(DFB)(λIR = 1541 nm). The two fibre outputs acted as a point like sources spaced by 27.9 μ m.
The first coupler output was used directly as a point-like source. To ensure the spatial incoherence of this binary star, a 500 m fibred delay line was inserted in the second path, to induce
an optical path difference longer than the 100 m coherence length of the DFB laser. The two
fibre ends were placed in the focal plane of a collimating lens with a 1900 mm focal length
and a 190 mm diameter. The resulting characteristics of our laboratory object corresponded to
a binary star with an Ω0 = 14.7 μ rad angular separation and an adjustable photometric ratio
(μ ). In our experimental configuration, the fluctuation of the air path between the star and the
telescopes, and the small mechanical vibrations of the test bench acted as the atmospheric turbulence in a real telescope array.
In our experiment, assuming point-like sources, we can theoretically describe the angular
intensity distribution of the object by:
O(Ω) =
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δ (Ω − Ω0 /2) + μδ (Ω + Ω0 /2)
(6)
Received 22 Feb 2011; revised 24 Mar 2011; accepted 24 Mar 2011; published 18 Apr 2011
25 April 2011 / Vol. 19, No. 9 / OPTICS EXPRESS 8621
with δ denoting the Dirac delta distribution. The angular Fourier Transform of Eq. (6) gives the
object spectrum Õ:
Õ(N) = exp (− jπ NΩ0 ) + μ exp ( jπ NΩ0 )
The resulting phase ϕi j for a given spatial frequency N can be written as:
μ −1
tan(π NΩ0 )
arg[Õ(N)] = arctan
μ +1
(7)
(8)
The phase closure φ is derived from Eq. (8) according to Eq. (5). Note that φ varies as a function of the μ parameter driven by the adjustable photometric ratio of our fibre coupler. In the
experimental setup, each telescope Ti was composed of an achromatic doublet ( f = 10 mm).
T1 T2 was fixed and spaced by a b = 16 mm separation. T3 can moved by steps equal to nb.
The optical fields, collected at each telescope focus, were fed into single-mode optical fibres
used as interferometric arms. Different optical path modulations had been applied to each interferometric arm in order to display the interferometric signal in the time domain. The Fourier
Transform of this interferometric signal was composed of three frequencies related to the three
pairs of telescopes. On each arm, a fibre coupler allowed to send 90% of the optical beam to
our upconversion interferometer. The remaining 10% are routed to a classical infrared interferometer previously developed by our team for the Multi Aperture Fibre Linked Interferometer
project [17] (bottom left Fig. 3). This infrared interferometer, used as a reference interferometer
in our set up, had demonstrated its accuracy and reliability for the acquisition of the complex
visibility of an infrared object.
In each arm of the upconversion interferometer, the infrared signal of the unbalanced binary star was mixed with a narrow-band pump source at 1064 nm and then injected in a PPLN
waveguide. Each Ti-indiffused waveguide of 40 mm used had a 11.3 μ m poling periodicity and
was temperature stabilized at about 90oC. This way, each signal was converted to a wavelength
of about 630 nm. Notice that we did not focus our study on the conversion efficiency, that has
been previously addressed for instance in [18, 19]. Each upconverted signal passed through
an interference filter to block the residual pump radiation and then fed a single-mode fibre at
630 nm. In each arm, the upconverted optical fields were combined together with an X-cube
(2002 patent 6363186 and [20]). This device had 4 inputs and 4 outputs. In our experimental
configuration, it had been used as a symmetrical 3 to 1 coupler for the visible radiation mixing.
The three upconverted interferometric arms were equalized. For this purpose the delay lines
were tuned and the interferometric pattern was detected with a silicon avalanche photodiode.
The raw data were analyzed to extract phase closure in the infrared and visible wavelengths at
the same time.
4.
Data acquisition processing and results
Figure 4 plots the phase terms as a function of time. As one can appreciate, the phase term
ϕ (Ti T j ), related to the pair of telescope Ti T j , is not constant over the time but the phase closure
remains constant over all the acquisition. The object was a point-like source and the data were
recorded with the infrared interferometer.
For the acquisition of the phase closure, in a first step, we had to calibrate the infrared and the
visible interferometer with a point-like source (one star was switched-off). The raw data coming from both interferometers were analyzed and calibrated. With a point-like star, the phase
closure is theoretically equal to 0. The Fourier Transform applied to the interferometric data
allowed to correct the experimental bias up to reach φ = 0.
In a second stage, the secondary star was switched-on and the phase closures were recorded
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Evolution of the phase terms as a function of time
3
Phase [rad]
2
φ(T1T2)
φ(T2T3)
φ(T3T1)
Φ
1
0
-1
-2
-3
0
10
20
30
40
50
Time [s]
60
70
80
Fig. 4. The Phase terms of a point-like source are plotted for the three pairs of telescopes
as a function of time. The phase closure term is the sum of the three phase terms.
for the infrared and the upconversion interferometers as a function of μ with a fixed baseline
configuration of the telescope array. These two stages had been realized for two configurations
of the telescope array (Fig. 5). In the first one, the distance between T1 T2 was equal to b and
T2 T3 was equal to 2b. In the second one, the distance between T1 T2 was equal to b and T2 T3
was equal to 3b. These measurements, obtained with the visible interferometer, were compared
with the theoretical data and with the infrared reference interferometer at the same time. Figure 5 shows an excellent accordance between theoretical predictions (green dashed curves) and
the upconversion (blue crosses) and classical interferometric (red crosses) data. The theoretical
curve is based on Eq. (8) and Eq. (5) written for a three-arm interferometer. Each experimental
point results from the average over a set of 30 phase closure acquisitions. The error bars (not
plotted) are on the order of 5 mrad and 10 mrad for the upconversion and the infrared interferometer respectively. These small uncertainties of the phase closure show the stability in time of
our upconversion interferometer. The error bars related to the photometric ratio μ are around
±3% for each point.
5.
Conclusion
This first proof-of-principle experiment clearly demonstrated that the phase closure can be
transferred without any distortion into the visible spectral domain by using our upconversion
interferometer. Being a key point for high resolution imaging, the phase closure acquisition
after frequency conversion clearly demonstrates the reliability of our upconversion interferometer capabilities. We have developed our upconversion interferometer using single-mode and
polarization maintaining components. To fit the astronomical observational constraints, we intend to operate our instrument with lower flux level (down to the photon-counting regime).
We also have to work on broadband frequency conversion. Preliminary study on this point
has already been realized [21] and we will have to adapt this technique in the high resolution
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Fig. 5. Phase closure measurements as a function of the photometric ratio μ for two configurations of the telescope array. On the left (right) hand side n=2(3). Red (blue) × plots
the infrared (visible) data. Green dashed curves report the theoretical data.
interferometric context. Further, this new kind of interferometer will be applied to frequency
conversion of broadband medium and/or far infrared spectra. In a more general way, the frequency conversion technique allows to benefit from mature optical components mainly used
in optical telecommunications (waveguides, couplers, multiplexers. . . ) and efficient low-noise
detection schemes down to the single-photon counting level. Consequently, it could be possible
to avoid lots of technical difficulties related to infrared optics (components transmission, thermal noises, thermal cooling, spatial filtering . . . ). The frequency conversion technique could be
used to have access to unexplored optical windows on ground observatories.
Acknowledgments
This work has been financially supported by the Centre National d’Etudes Spatiales (CNES)
and by l’Institut National des Sciences de L’Univers (INSU). Our thanks go to A. Dexet for the
development and his advices for all the specific mechanical components.
#143071 - $15.00 USD
(C) 2011 OSA
Received 22 Feb 2011; revised 24 Mar 2011; accepted 24 Mar 2011; published 18 Apr 2011
25 April 2011 / Vol. 19, No. 9 / OPTICS EXPRESS 8624